Kinetics of template-directed multistate copolymerization
Abstract
We consider processes of template-directed multistate copolymerization by molecular machines such as polymerases or ribosomes, having multiple states of conformation or activation. We show that the kinetic equations of these processes can be exactly solved for the mean growth velocity, the sequence probabilities of the grown copy, and the local probabilities and fractions of monomeric units in the copy. Asymptotically, in the long-time limit, the kinetic equations are solved with a matrix factorization ansatz in terms of a backward iteration, forming an iterated matrix function system, and a complementary forward iteration, both running along the template sequence. The iterative method is very significantly faster than usual computational methods, as demonstrated with a numerical example.
Versions
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BibTeX
@misc{gaspard2026kinetics,
title = {{Kinetics of template-directed multistate copolymerization}},
author = {Pierre Gaspard},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.22448},
eprint = {2606.22448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.22448},
}
RIS
TY - UNPB
TI - Kinetics of template-directed multistate copolymerization
AU - Pierre Gaspard
PY - 2026
DA - 2026/06/21
PB - arXiv
DO - 10.48550/arxiv.2606.22448
UR - https://arxiv.org/abs/2606.22448
AB - We consider processes of template-directed multistate copolymerization by molecular machines such as polymerases or ribosomes, having multiple states of conformation or activation. We show that the kinetic equations of these processes can be exactly solved for the mean growth velocity, the sequence probabilities of the grown copy, and the local probabilities and fractions of monomeric units in the copy. Asymptotically, in the long-time limit, the kinetic equations are solved with a matrix factorization ansatz in terms of a backward iteration, forming an iterated matrix function system, and a complementary forward iteration, both running along the template sequence. The iterative method is very significantly faster than usual computational methods, as demonstrated with a numerical example.
ER -